The question lingers as to what exactly "lab-administered" means. When I've done CVS/Walgreens tests I pulled up to the drive through, swabbed my own nose, handed my "test kit" to a cashier, and drove out. To me that's not any more "lab-administered" than a proctored at-home test.
I'll bet people will be able to board using the at-home proctored method but I wouldn't want to bet my vacation on it. Hopefully someone here on the boards will "take on for the team" and try the proctored method after Aug 29th to possibly give us more clarity on this.